Positron emission tomography (PET) has been shown to be useful in the diagnosis of a wide variety of neurological and cardiac diseases. For neurological imaging, dedicated brain scanners have the advantages of increased sensitivity and better spatial resolution due to their reduced apterture size and detector separation. We propose the design and construction of a prototype dedicated brain scanner which will have significant advantages for clinical neurological imaging. The scanner is based on the use of a detector composed of a single, continuous cylindrical NaI(T1) crystal. This crystal, 65 cm in diameter and 21 cm in its axial extent, would be coupled to approximately 160 photomultipliers to yield a tomographic with a useful axial field-of- view of at least 12 cm and 2 mm data sampling along all three image axes. The use of a single NaI(T1) crystal results not only in dramatically reduced system complexity and cost, but also in good spatial, timing, and energy resolution. In Phase I of the project, the feasibility of manufacturing the cylindrical crystal and of detecting coincidences in a single continuous crystal were demonstrated. In Phase II, we intend to construct and test a prototype of the single-crystal tomograph.